For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant:
(a) 2 H₂O(g) → 2 H₂(g) + O₂(g)
(b) 2 SO₂(g) + O₂(g) → 2 SO₃(g)
(c) 2 NO(g) + 2 H₂(g) → N₂(g) + 2 H₂O(g) (d) N₂(g) + 2 H₂(g) → N₂H₄(g)

Verified step by step guidance

1. Identify the balanced chemical equation: \(2 \text{H}_2\text{O}(g) \rightarrow 2 \text{H}_2(g) + \text{O}_2(g)\).
2. Determine the rate of disappearance of the reactant: The rate of disappearance of \(\text{H}_2\text{O}\) is \(-\frac{1}{2} \frac{d[\text{H}_2\text{O}]}{dt}\).
3. Determine the rate of appearance of the products: The rate of appearance of \(\text{H}_2\) is \(+\frac{1}{2} \frac{d[\text{H}_2]}{dt}\).
4. Determine the rate of appearance of the products: The rate of appearance of \(\text{O}_2\) is \(+\frac{d[\text{O}_2]}{dt}\).
5. Relate the rates of disappearance and appearance: \(-\frac{1}{2} \frac{d[\text{H}_2\text{O}]}{dt} = +\frac{1}{2} \frac{d[\text{H}_2]}{dt} = +\frac{d[\text{O}_2]}{dt}\).

Key Concepts

Rate of Reaction

The rate of a chemical reaction is a measure of how quickly reactants are converted into products. It is typically expressed as the change in concentration of a reactant or product over time. In gas-phase reactions, this can be quantified using the stoichiometry of the balanced equation, which indicates how the concentrations of reactants and products change as the reaction proceeds.

Stoichiometry

Stoichiometry refers to the quantitative relationship between the amounts of reactants and products in a chemical reaction, as dictated by the balanced chemical equation. It allows us to determine the coefficients that represent the molar ratios of substances involved, which are essential for writing rate expressions that accurately reflect the changes in concentration of each species during the reaction.

Rate Expression

A rate expression is a mathematical representation of the rate of a chemical reaction in terms of the concentrations of reactants and products. It is formulated based on the stoichiometry of the reaction, where the rate is expressed as the change in concentration of products divided by the change in concentration of reactants, each raised to the power of their respective coefficients in the balanced equation.